A052878 E.g.f.: log((1-x)/(1-3*x+x^2)).

0, 2, 6, 34, 276, 2928, 38520, 606240, 11118240, 232928640, 5488922880, 143707737600, 4138613740800, 130021152307200, 4425207423436800, 162194949242726400, 6369480464675328000, 266808295408951296000, 11874724735152254976000, 559591803705456377856000

Offset

0,2

Comments

Previous name was: A simple grammar.

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 849

Formula

Recurrence: {a(1)=2, a(2)=6, a(3)=34, (-n^3-2*n-3*n^2)*a(n)+(4*n^2+12*n+8)*a(n+1)+(-4*n-8)*a(n+2)+a(n+3)}

For n > 0, a(n) = (n-1)! * (phi^(2*n) + 1/phi^(2*n) - 1), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 06 2019

Maple

spec := [S, {B=Sequence(Z, 1 <= card), C=Union(Z, B), S=Cycle(C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
with(combinat):
0, seq( (fibonacci(2*n+1)+fibonacci(2*n-1)-1) * (n-1)!, n=1..20);  # Mark van Hoeij, May 29 2013

Prog

(PARI)  x='x+O('x^66); concat([0], Vec(serlaplace(log(-(-1+x)/(1-3*x+x^2))))) \\ Joerg Arndt, May 29 2013

Crossrefs

Sequence in context: A262391 A271212 A325296 * A168362 A274711 A076863

Adjacent sequences: A052875 A052876 A052877 * A052879 A052880 A052881

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

New name using e.g.f., Vaclav Kotesovec, Jun 06 2019

Status

approved